@EdelingF
From your OP
But the only problem is to get connect the servers to the internet. I mean, to make the servers 'visible' from outside my network. I thought, no problem, just make some changes in the modem/router like I did with my old server by using port-forwarding. Wrong!
I thought, no problem,
Correct!!
You should have been able to PF to the new server without problem/issue.
My guess is you might not have removed the old PF first and you had two port 80 PF's.
Which won't work.
IOW One port -- only one port forward for that port i.e. 80.
I found out I need something like a reverse proxy.
Maybe!!
Unless of course you have some special case or issue, which is not clear at this point.
Keep in mind, with a proxy you still may need to do some redirect dirty work on the proxy, depends on what your trying to accomplish.
hth